Neural Network Artificial Intelligence

Question

In a simple perception, can someone explain to me the concept of the Threshold and and how to set it, i.e. initially what is the value of the Threshold input and weight??

Answer 1

Since by definition the perceptron is a binary classifier even in it's simplest incarnation you can think of it as having a bias/threshold of 0:
y = f( w_n* x_n> 0 ? 1 : 0 )
But since 0 is a pretty arbitrary value the bias/threshold is explicitly introduced into the model as a variable:
y = f( w_n* x_n> b^'? 1 : 0 ) or y = f( w_n* x_n+ b > 0 ? 1 : 0 )
The problem is that now the model another variables (b [which is a scalar] apart from the original w_n [which is a vector]) that needs to be taken into account when training.
There are many ways to do that, the naive way being to just pick some of the possible values of b and for each train the model on w_n and keep the ( b, w_n) pair that produced the best result.
A more elegant way is to just think of the bias/threshold variable b as being a weight that is attached to an input that is always 1 which basically brings the model back to the original form with only 1 variable w except that now the vectors x and w have n + 1 elements:
y = f( w_{n + 1}* x_{n + 1}> 0 ? 1 : 0 )